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Every time you write "1 atm = 76 cm of mercury" you are using an experiment from 1643. This post explains what Evangelista Torricelli did, the simple physics that sets the height of a barometer, his law for liquid flowing out of a tank, and the habits behind his work.
Who was Torricelli?
Torricelli was born in Faenza, Italy, on 15 October 1608 and died in Florence on 25 October 1647, according to the MacTutor biography from the University of St Andrews. He came from a poor family, studied with the mathematician Benedetto Castelli in Rome, and worked as his secretary. In October 1641 he went to live with Galileo at Arcetri as his assistant. Galileo died a few months later, in January 1642, and Torricelli succeeded him as court mathematician to the Grand Duke of Tuscany.
He was also a skilled lens grinder and made telescopes. MacTutor reports that one of his lenses, examined in 1924, was found to be of exceptionally fine workmanship.
What problem was Torricelli trying to solve?
Pump makers knew that a suction pump could lift water only about nine metres. Galileo had noticed this but explained it with a "force created by a vacuum", MacTutor notes. At the time, many scholars held that nature does not allow a vacuum at all.
Torricelli guessed the limit had a different cause: the weight of the air pressing on the water outside the pump. If so, a heavier liquid should rise less. Mercury is about 13.6 times denser than water, so it should stop at about one thirteenth of the height.
What did the mercury experiment show?
In 1643 Torricelli proposed the experiment, which his colleague Vincenzo Viviani carried out. In a letter to Michelangelo Ricci dated 11 June 1644, quoted in translation by MacTutor, Torricelli described glass tubes about two cubits long, filled with mercury, closed with a finger, turned upside down and opened under the surface of a bowl of mercury. The mercury fell part of the way and left an empty space at the top.
His explanation was the new part. He argued that the force holding the mercury up came from outside the tube: the weight of the air resting on the mercury in the bowl. In his words, in MacTutor's translation, it "should rise in a column high enough to make equilibrium with the weight of the external air which forces it up".
The same letter shows he already saw a use for it: an instrument "which will exhibit changes in the atmosphere". That is the barometer. The old unit of pressure, the torr, is named after him; one torr is 133.3224 Pa, the same as the conventional millimetre of mercury (NIST SP 811, Appendix B.8).
Worked example: why 76 cm of mercury, and about 10 m of water?
At the top of the column the pressure is almost zero. At the level of the bowl it equals atmospheric pressure. So p = ρgh.
Standard atmospheric pressure is 101,325 Pa (NIST).
For mercury, take ρ = 13,600 kg/m³ and g = 9.81 m/s². Then h = 101,325 ÷ (13,600 × 9.81) ≈ 0.760 m.
For water, ρ = 1,000 kg/m³, so h = 101,325 ÷ (1,000 × 9.81) ≈ 10.3 m.
The water figure explains the pump makers' limit. A suction pump cannot lift water higher than the atmosphere can push it, and the practical limit is a little lower because pumps are not perfect.
Common mistakes to avoid:
Thinking the tube's width matters. It does not. Pressure depends on depth, not on the cross-section, so a wide tube and a narrow tube stand at the same height.
Measuring along a tilted tube. If the tube leans, the mercury runs further along it, but the vertical height stays at about 76 cm.
Mixing units. Convert cm to m before using p = ρgh in SI units.
What is Torricelli's theorem?
In *De motu gravium*, part of his *Opera geometrica* of 1644, Torricelli proved that liquid flows out through an opening at a rate proportional to the square root of the height of liquid above it, MacTutor records. In modern form the speed is v = √(2gh), the same speed a body would gain falling freely through h.
Example. A tank has a small hole 0.80 m below the water surface. The speed of the jet is v = √(2 × 9.8 × 0.80) = √15.68 ≈ 3.96 m/s.
Today you can derive this from Bernoulli's principle, which the JEE Main and NEET-UG syllabi both list. Our guide to pressure, buoyancy and Bernoulli's equation covers the usual traps, such as forgetting that the tank's surface is also at atmospheric pressure.
What can you learn from Torricelli?
Explain a limit, do not just accept it. The nine-metre rule was known. Torricelli asked what caused it.
Use a second case to test your idea. Swapping water for a liquid 13.6 times denser is a clean test: the column should shrink by the same factor.
Follow your teachers, then go past them. He finished Galileo's line of work on motion and also corrected Galileo's explanation of the pump.
Pascal took the next step and carried a Torricelli tube up a mountain; read the story in our post on Blaise Pascal and the Puy de Dôme experiment. If you want to see how depth and density change pressure before you calculate, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read.
Try this today: work out how tall a barometer filled with cooking oil of density 920 kg/m³ would need to be.
